A STUDY ON GROUP PROPERTIES, GROUP ISOMORPHISM AND ITS APPLICATIONS

ABSTRACT

In group theory, a branch of mathematics, the term order is used in two closely-related senses:

·         The order of a group is its cardinality, i.e., the number of its elements.

·         The order, sometimes period, of an element a of a group is the smallest positive integer m such that a   m = e (where e denotes the identity element of the group, and am denotes the product of m copies of a). If no such m exists, a is said to have infinite order. All elements of finite groups have finite order. We determine all the ways to find out order of finite and infinite group. The order of a group G is denoted by ord(G) or |G| and the order of an element a by ord (a) or |a|.

FULL TEXT